By Byrn Stole

BATON ROUGE, La. (Reuters) - Emergency crews in Louisiana have rescued more than 7,000 people stranded by historic flooding that has killed at least three and submerged whole communities, Governor John Bel Edwards said on Sunday, as the parts of the U.S. Gulf Coast braced for more rain and rising waters.

Residents have been pulled out of flooded homes, swamped cars and threatened medical facilities in cities and towns across the southern part of the state, said Edwards, who has called for federal emergency relief funds.

While the brunt of the storm that brought torrential rains and flooding to the area was moving west toward Texas on Sunday, Louisiana residents should remain cautious, the governor said at a news conference.

"Even with the sunshine out today intermittently, the waters are going to continue to rise in many areas, so this is no time to let the guard down," Edwards said.

Some 5,000 people were forced to sleep in shelters overnight, said Marketa Walters, head of Louisiana Department of Children and Family Services. There were not enough beds to house all of the shelter-seekers, so many had to sleep on floors, she said.

Emergency officials still were working on strategies to rescue an undetermined number of people trapped by the waters.

"We're very much still in the search and rescue mode," said James Waskcom, director of the state's Office of Homeland Security and Emergency Preparedness.

Patients from several hospitals and nursing homes were saved from threatening waters overnight, Louisiana State Police Colonel Michael Edmonson said. Helicopters are deploying food and water to those still trapped by floods, he said.

Many roadways have been closed or blocked off by water and debris, said Shawn Wilson, the state's transportation secretary. About 1,400 bridges will need to be inspected for damage before being deemed safe for use, he said.

Some 1,700 members of the Louisiana National Guard have been deployed throughout the southern part of the state for rescue efforts and that number is expected to rise to 2,500 as requests for aid roll in.

Meanwhile, downpours threatened to trigger floods further south in the state and west into Texas.

The National Weather Service (NWS) on Sunday maintained a flash flood watch for parts of Louisiana and Mississippi and extended it to southeastern Texas, including the city of Houston, where rains killed at least eight in late April.

More rains were expected in southern Louisiana, with NWS forecasting on its website that another 2-6 inches (5-15 cm) were possible on Sunday night in some areas, while 2-4 inches could fall in others and in parts of Texas.

Edwards, who described the flooding as unprecedented and historic, said he was awaiting a response to his request that the Federal Emergency Management Agency (FEMA) make a federal disaster declaration for affected areas of the state.

In addition to the three dead in the flooding, another person is believed to be missing in St. Helena Parish, northeast of Baton Rouge near the Mississippi border, Edwards said.

On Saturday, the body of a woman was recovered from the Tickfaw River, also in St. Helena Parish, after a car in which she was riding was swept away by flood waters. Rescuers found her husband and mother in law clinging to a tree.

A 54-year-old man in Greensburg in the northern part of the state died when his vehicle was swept off the road, state police said.

The body of a 68-year-old man was recovered on Friday near Baker after he drowned while trying to evacuate, said William "Beau" Clark, the coroner in East Baton Rouge Parish.

(Additional reporting by Laila Kearney and Chris Prentice in New York; Editing by Alan Crosby and Bill Trott)